Grass clippings make a great organic mulch material and as they decompose they actually release some nitrogen into the soil. The only potential problem with using fresh grass clippings in the flower beds is that they tend to form a thick layer until they begin to decompose and that thick layer can actually shed water. To counteract that you only need to remember to rake the clumps occasionally to spread the grass clippings out. Aside from that, flower gardens are a great place to recycle your grass clippings.